Problem: Rewrite as a simplified fraction. ${0.63\overline{8} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 638.8888...\\ 100x &= 63.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 575}$ ${x = \dfrac{575}{900}} $ ${x = \dfrac{23}{36}} $